1. Field of the Invention
The present invention relates to a method and a program for designing semiconductor integrated circuits and a semiconductor integrated circuit designing apparatus, and particularly to a designing method, a program, and a semiconductor integrated circuit designing apparatus that utilize timing analysis using statistical techniques.
2. Description of the Background Art
FIG. 11 is a schematic diagram illustrating the concept of Static Timing Analysis (STA) that is known as a method of timing analysis of semiconductor integrated circuits.
FIG. 11 exemplifies a semiconductor integrated circuit having 15 nodes from ND0 to ND14. Nodes are defined herein as elements having delays, such as logic gates and interconnections, and it is assumed that the nodes ND4, ND6, and ND10 are flip-flops, the nodes ND5, ND7 to ND9 are AND logic gates, and the other nodes are unspecified logic gates.
In the static timing analysis, the results of analysis are represented with coefficients that are set to correct delay variations caused by an on-chip variation (OCV), one of element characteristic variations. As shown in FIG. 11, the correcting coefficients, by which the reference delays of nodes are to be multiplied, are calculated respectively for the arrival paths (data paths) and required paths (clock paths).
In FIG. 11, the arrival paths include two paths: a path passing from the node ND0 to the node ND10 through the nodes ND1 to ND4 and ND7 to ND9; and a path passing from the node ND2 to the node ND6 through the nodes ND3 to ND5, and the required paths include two paths: a path passing from the node ND0 to the node ND10 through the nodes ND12 to ND14; and a path passing from the node ND2 to the node ND6 through the node ND11.
The arrival paths and the required paths can be provided with coefficients individually. FIG. 11 shows an example of analysis in which the on-chip variation is regarded as ±6%, and the coefficient for the arrival paths is set as reference delay×1.06 (+6%) and the coefficient for the required paths is set as reference delay×0.94 (−6%).
FIG. 12 is a schematic diagram illustrating the concept of statistical STA that is known as another method of timing analysis.
The semiconductor integrated circuit of FIG. 12 has the same node structure as that of FIG. 11, and the same components as those of the semiconductor integrated circuit of FIG. 11 are shown at the same reference characters and are not described again.
As shown in FIG. 12, in the statistical STA, by considering variations, delays are handled as distributions, and the delay at each node is assumed to be a normal distribution and represented with a mean and a standard deviation, so as to conduct propagation analysis with normal distributions.
It is thought that on-chip variation components, particularly random variation components, become larger as the miniaturization of semiconductor process advances. Accordingly, if the value of on-chip variation is set too large in the design process in order to cover all possible circuit configurations, more margins than necessary will be ensured and performance and design convergence of semiconductor integrated circuits will be deteriorated.
On the other hand, if the on-chip variation value is set too small in design, necessary margin cannot be ensured and the possibility of malfunctions will increase.
As described referring to FIG. 11, the conventional static timing analysis assumes the on-chip variation correcting coefficients at fixed values, and the analysis is therefore unable to accurately provide random variation components that are statistically cancelled depending on the circuit configuration.
As disclosed in Japanese Patent Application Laid-Open No. 2005-122298 (FIGS. 3 and 4), a method is suggested in which the random variation component is calculated in accordance with the number of cell stages (the number of gate stages), but the method considers arrival and required paths separately and therefore involves unnecessary margins.
On the other hand, the statistical STA offers more realistic computation results because it represents delays with normal distributions and considers random variation components etc. in a statistical manner. However, the statistical STA takes a longer processing time than STA and at present cannot be applied to design of large-scale semiconductor integrated circuits.